This paper introduces an efficient and generic framework for finite-element simulations under an implicit time integration scheme. Being compatible with generic constitutive models, a fast matrix assembly method exploits the fact that system matrices are created in a deterministic way as long as the mesh topology remains constant. Using the sparsity pattern of the assembled system brings about significant optimizations on the assembly stage. As a result, developed techniques of GPU-based parallelization can be directly applied with the assembled system. Moreover, an asynchronous Cholesky precondition scheme is used to improve the convergence of the system solver. On this basis, a GPU-based Cholesky preconditioner is developed, significantly reducing the data transfer between the CPU/GPU during the solving stage. We evaluate the performance of our method with different mesh elements and hyperelastic models and compare it with typical approaches on the CPU and the GPU.

翻译：本文提出了一种用于隐式时间积分方案下有限元仿真的高效通用框架。该框架兼容通用本构模型，采用快速矩阵组装方法，利用当网格拓扑结构保持不变时系统矩阵以确定性方式生成的特性。通过利用组装系统的稀疏模式，在矩阵组装阶段实现了显著的优化。这使得基于GPU的并行化技术可直接应用于组装后的系统。此外，采用异步Cholesky预处理方案来改善系统求解器的收敛性。在此基础上，开发了基于GPU的Cholesky预处理器，显著减少了求解阶段CPU/GPU之间的数据传输。我们使用不同网格单元和超弹性模型评估了所提方法的性能，并将其与CPU和GPU上的典型方法进行了对比。